March 14th, 2009, 09:42 PM  #1 
Member Joined: Feb 2009 Posts: 76 Thanks: 0  level surfaces of function
How do you describe the level surface of this function f(x,y,z) = x^(2) + 3y^(2)+ 5z^(2) This seems like a family of ellipsoids but I really dont know for sure. 
March 15th, 2009, 12:50 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: level surfaces of function
That's correct. Rearranging, it looks like this: When c is positive, this level surface is an ellipsoid. 

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